BTGModeratorVI wrote: ↑

Wed Feb 03, 2021 10:30 am

In xy-coordinate plane, lines j and k intersect at the point (5, 0). If both lines have defined slopes, is the y-intercept of line j greater than the y-intercept of line k?

1) The slope of line k is greater than the slope of line j.
2) Line j has a negative slope

Answer: A
Source: GMAT prep now

Target question: Is the y-intercept of line j greater than the y-intercept of line k?

Statement 1: The slope of line k is greater than the slope of line j.
Let's examine 2 cases: the slope of line j is positive and the slope of line j is negative
Case a: the slope of line j is positive

Notice that, if line k has a greater slope, then the y-intercept of line j IS greater than the y-intercept of line k

Case b: the slope of line j is negative
ASIDE: Some students will misinterpret statement 1 to suggest that line k is steeper than link j. However, this is true ONLY WHEN line j has a positive slope. The opposite is true when line j has a negative slope.
To help visualize this, I have made slope of line j equal to -1

Notice that a slope of -2/3 is greater than a slope of -1
And a slope of -1/8 is greater than a slope of -1
As we can see, in all cases, the y-intercept of line j IS greater than the y-intercept of line k

Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: Line j has a negative slope
This statement is NOT sufficient.
Consider the following two cases:

In the above case, the y-intercept of line j is GREATER than the y-intercept of line k


In the above case, the y-intercept of line j is LESS than the y-intercept of line k
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A